We consider the estimation problem for jointly stable random variables. Under two specific dependency models: a linear transformation of two independent stable variables and a sub-Gaussian symmetric $α$-stable (S$α$S) vector, we show that the conditional mean estimator is linear in both cases. Moreover, we find dispersion optimal linear estimators. Interestingly, for the sub-Gaussian (S$α$S) vector, both estimators are identical generalizing the well-known Gaussian result of the conditional mean being the best linear minimum-mean square estimator.

翻译：我们考虑联合稳定随机变量的估计问题。在两种特定的依赖模型下：两个独立稳定变量的线性变换以及次高斯对称α稳定(SαS)向量，我们证明了在这两种情况下条件均值估计器都是线性的。此外，我们找到了离散度最优的线性估计器。值得注意的是，对于次高斯(SαS)向量，这两种估计器是相同的，这推广了条件均值即最优线性最小均方估计器这一著名的高斯结果。